Or Korra could be the name of the water bender that is the next incarnation of the Avatar.
Well that brings up the question of whether bending is a genetic thing, specific to certain ethnicities, or if it's simply something that can manifest in anyone anywhere, and only the "right" kind of benders are recognized, encouraged, and trained, depending on the culture. Like, if someone in the water tribes has the inate skill to fire bend, they'll never know it because, fuck that, there'll be no fire bending there - you'll be a water bender or nothing, mister, and you'll like it.
I have to believe it's more cultural than anything else, as they're all pretty obviously the same species. In which case, I'd have to assume Aang amd subsequent avatars would be travelling the world, seeking out possible airbenders anywhere they could find them. You sure aren't going to establish a viable breeding population based on the genetic material of one little dude.